Profinite completion of Grigorchuk's group is not finitely presented

Abstract

In this paper we prove that the profinite completion $\hat{\mathcal{G}}$ of the Grigorchuk group $\mathcal{G}$ is not finitely presented as a profinite group. We obtain this result by showing that $H^2(\mathcal{\hat G},\field{F}_2)$ is infinite dimensional. Also several results are proven about the finite quotients $\mathcal{G}/S{t}_{\mathcal{G}}(n)$ including minimal presentations and Schur Multipliers.

References in corpus (1)

• The Twisted Twin of the Grigorchuk Group